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A Simple Quantifier-Free Formula of Positive Semidefinite Cyclic Ternary Quartic Forms

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Computer Mathematics

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Abstract

The problem of quantifier elimination of positive semidefinite cyclic ternary quartic forms is studied in this paper. We solve the problem by function RealTriangularize in Maple15, the theory of complete discrimination systems and the so-called Criterions on Equality of Symmetric Inequalities method. The equivalent simple quantifier-free formula is proposed, which is difficult to obtain automatically by previous methods or quantifier elimination tools.

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Acknowledgments

This research was partly supported by President’s Fund for Undergraduate Students of Peking University, NSFC-11271034 and the project SYSKF1207 from ISCAS. The author would like to thank the anonymous referees for their valuable comments on a previous version of this paper.

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Authors and Affiliations

  1. Beijing International Center for Mathematical Research and School of Mathematical Sciences, Peking University, Beijing, China

    Jingjun Han

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  1. Jingjun Han
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Correspondence to Jingjun Han .

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Editors and Affiliations

  1. Academy of Mathematics & System Science, Beijing, China

    Ruyong Feng

  2. Department of Mathematics and Computer S, University of Antwerp, Antwerp, Antwerpen, Belgium

    Wen-shin Lee

  3. Department of Mathematical Information S, Tokyo University of Science, Tokyo, Tokyo, Japan

    Yosuke Sato

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Han, J. (2014). A Simple Quantifier-Free Formula of Positive Semidefinite Cyclic Ternary Quartic Forms. In: Feng, R., Lee, Ws., Sato, Y. (eds) Computer Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-43799-5_20

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